The purpose of the present work is to determine initial conditions that generate reacting, recrossing-free trajectories that cross the conventional dividing surface of transition state theory (i.e., the ... [more ▼]

The purpose of the present work is to determine initial conditions that generate reacting, recrossing-free trajectories that cross the conventional dividing surface of transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) without ever returning to it. Local analytical equations of motion valid in the neighborhood of this planar surface have been derived as an expansion in Poisson brackets. We show that the mere presence of a saddle point implies that reactivity criteria can be quite simply formulated in terms of elements of this series, irrespective of the shape of the potential energy function. Some of these elements are demonstrated to be equal to a sum of squares and thus to be necessarily positive, which has a profound impact on the dynamics. The method is then applied to a three-dimensional model describing an atom-diatom interaction. A particular relation between initial conditions is shown to generate a bundle of reactive trajectories that form reactive cylinders (or conduits) in phase space. This relation considerably reduces the phase space volume of initial conditions that generate recrossing-free trajectories. Loci in phase space of reactive initial conditions are presented. Reactivity is influenced by symmetry, as shown by a comparative study of collinear and bent transition states. Finally, it is argued that the rules that have been derived to generate reactive trajectories in classical mechanics are also useful to build up a reactive wave packet. [less ▲]

We consider a triatomic system with zero total angular momentum and demonstrate that, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of ... [more ▼]

The objective of the present paper is to show the existence of motion coordination among a bundle of trajectories crossing a saddle point region in the forward direction. For zero total angular momentum ... [more ▼]

In the vicinity of a transition state, the dynamics is constrained by approximate local invariants of the motion even if the potential energy surface is anharmonic. The concept of local regularity near a ... [more ▼]

A point charge interacting with a dipole (either induced or permanent) constitutes a completely integrable dynamical subsystem characterized by three first integrals of the motion (E, pφ, and either 2 or ... [more ▼]

In a two-dimensional space where a point particle interacts with a diatomic fragment, the action integral Φ pθ dθ (where θ is the angle between the fragment and the line of centers and pθ its conjugate ... [more ▼]

in International Journal of Quantum Chemistry (2008), 108(10), 1629-1636

When the dynamics is constrained by adiabatic invariance, a reactive process can be described as a one-dimensional motion along the reaction coordinate in an effective potential. This simplification is ... [more ▼]

Kinetic energy release distributions (KERDs) for the benzene ion fragmenting into C4H4+ and C2H2 have been recorded by double-focussing mass spectrometry in the metastable energy window and by a retarding ... [more ▼]

Kinetic energy release distributions (KERDs) for the benzene ion fragmenting into C4H4+ and C2H2 have been recorded by double-focussing mass spectrometry in the metastable energy window and by a retarding field experiment up to an energy of 5 eV above the fragmentation threshold. They are compared with those resulting from the HCN loss reaction from the pyridine ion. Both reactions display a similar variation of the kinetic energy release as a function of the internal energy: the average release is smaller than statistically expected, with a further restriction of the phase-space sampling for the C5H5N+ dissociation. Ab initio calculations of the potential-energy profile have been carried out. They reveal a complicated reaction mechanism, the last step of which consists in the dissociation of a weakly bound ion-quadrupole or ion-dipole complex. The KERDs have been analyzed by the maximum entropy method. The fraction of phase-space effectively sampled by the pair of fragments has been determined and is similar for both dissociations. Both reactions are constrained by the square root of the released kinetic energy, epsilon1/2. This indicates that in the latter stage of the dissociation process, the reaction coordinate is adiabatically decoupled from the bath of the bound degrees of freedom. For the C6H6+ fragmentation, the analysis of the experimental results strongly suggests that, just as for the symmetric interaction potential, the translational motion is confined to a two-dimensional subspace. This dimensionality reduction of the translational phase space is due to the fact that the Hamiltonian of both weakly bound complexes contains a cyclic coordinate. [less ▲]

For long-range electrostatic potentials and, more generally, when the topography of the potential energy surface is locally simple, the reaction path coordinate is adiabatically separable from the ... [more ▼]

For long-range electrostatic potentials and, more generally, when the topography of the potential energy surface is locally simple, the reaction path coordinate is adiabatically separable from the perpendicular degrees of freedom. For the ion-permanent dipole and ion-quadrupole interactions, the Poisson bracket of the adiabatic invariant decreases with the interfragment distance more rapidly than the electrostatic potential. The smaller the translational momentum, the moment of inertia of the neutral fragment, and the dipole or quadrupole moments are, the more reliable the adiabatic approximation is, as expected from the usual argumentation. Closed-form expressions for an effective one-dimensional potential in an adiabatic Hamiltonian are given. Connection with a model where the decoupling is exact is obtained in the limit of an infinitely heavy dipole. The dynamics is also constrained by adiabatic invariance for a harmonic valley about a curved reaction path, as shown by the reaction path Hamiltonian method. The maximum entropy method reveals that, as a result of the invariance properties of the entropy, constraints whose validity has been demonstrated locally only subsist in all parts of phase space. However, their form varies continuously, and they are not necessarily expressed in simple terms as they are in the asymptotic region. Therefore, although the influence of adiabatic invariance has been demonstrated at asymptotically large values of the reaction coordinate only, it persists in more interesting ranges. [less ▲]

The kinetic energy release distributions (KERDs) associated with the hydrogen loss from the benzene cation and the deuterium loss from the perdeuteriobenzene cation have been remeasured on the metastable ... [more ▼]

The kinetic energy release distributions (KERDs) associated with the hydrogen loss from the benzene cation and the deuterium loss from the perdeuteriobenzene cation have been remeasured on the metastable time scale and analyzed by the maximum entropy method. The experimental kinetic energy releases are larger than expected statistically, in contradistinction to what has been observed for the C-X fragmentations of the halogenobenzene cations. H(D) loss from C6H6+ (C6D6+) occurs via a conical intersection connecting the (2)A(2) and (2)A(1) electronic states. Two models are proposed to account for the experimental data: (i) a modified orbiting transition state theory (OTST) approach incorporating electronic nonadiabaticity; (ii) an electronically nonadiabatic version of the statistical adiabatic channel model ( SACM) of Quack and Troe. The latter approach is found to be preferable. It leads to the conclusion that the larger the energy stored in the transitional modes, which partly convert to the relative interfragment motion, the shorter the value of the reaction coordinate at which the adiabatic channels cross, and the larger the probability of undergoing the (2)A(2) -> (2)A(1) transition required for hydrogen loss. [less ▲]

Energy is not always fully randomized in an activated molecule because of the existence of dynamical constraints. An analysis of kinetic energy release distributions (KERDs) of dissociation fragments by ... [more ▼]

Energy is not always fully randomized in an activated molecule because of the existence of dynamical constraints. An analysis of kinetic energy release distributions (KERDs) of dissociation fragments by the maximum entropy method (MEM) provides information on the efficiency of the energy flow between the reaction coordinate and the remaining degrees of freedom during the fragmentation. For example, for barrierless cleavages, large translational energy releases are disfavoured while energy channeling into the rotational and vibrational degrees of freedom of the pair of fragments is increased with respect to a purely statistical partitioning. Hydrogen atom loss reactions provide an exception to this propensity rule. An ergodicity index, F, can be derived. It represents an upper bound to the ratio between two volumes of phase space: that effectively explored during the reaction and that in principle available at the internal energy E. The function F(E) has been found to initially decrease and to level off at high internal energies. For an atom loss reaction, the orbiting transition state version of phase space theory (OTST) is especially valid for low internal energies, low total angular momentum, large reduced mass of the pair of fragments, large rotational constant of the fragment ion, and large polarizability of the released atom. For barrierless dissociations, the major constraint that results from conservation of angular momentum is a propensity to confine the translational motion to a two-dimensional space. For high rotational quantum numbers, the influence of conservation of angular momentum cannot be separated from effects resulting from the curvature of the reaction path. The nonlinear relationship between the average translational energy <epsilon > and the internal energy E is determined by the density of vibrational-rotational states of the pair of fragments and also by non-statistical effects related to the incompleteness of phase space exploration. The MEM analysis of experimental KERDs suggests that many simple reactions can be described by the reaction path Hamiltonian (RPH) model and provides a criterion for the validity of this method. Chemically oriented problems can also be solved by this approach. A few examples are discussed: determination of branching ratios between competitive channels, reactions involving a reverse activation barrier, nonadiabatic mechanisms, and isolated state decay. (c) 2005 Elsevier B.V. All rights reserved. [less ▲]

Conversion of translational into vibrational energy during the last step of a unimolecular reaction is brought about by the curvature of the reaction path. The corresponding coupling is analyzed by an ... [more ▼]

Conversion of translational into vibrational energy during the last step of a unimolecular reaction is brought about by the curvature of the reaction path. The corresponding coupling is analyzed by an angle-action reaction path Hamiltonian (RPH). The accuracy of the vibrational adiabatic approximation is found to be completely independent of the shape of the potential energy V(s). Vibrations are adiabatic when two independent dimensionless parameters are small. The first one, denoted as sigma, controls the dynamic coupling. The physical significance of the condition sigma << 1 is that the amplitude of the vibrations normal to the reaction path should be much smaller than the radius of curvature of the reaction path. The second parameter, denoted as mu, governs the static coupling. It results from the dependence of the vibrational frequency omega on the reaction coordinate s. The higher omega, the lower its derivative with respect to s and, more unexpectedly, the higher the translational energy epsilon, the lower mu is. A criterion for locating a particular dividing surface in barrierless reactions is proposed. This surface separates two regions of space: one where energy flows freely, and one where energy conversion between translation and vibration is hindered by adiabatic invariance. The nature of the dynamical constraint that prevents the product translational energy distribution from being fully statistical can be identified by a maximum entropy analysis. The constraint is found to bear on the translational momentum p(s), i.e., on the square root of the translational energy epsilon(1/2). This can be understood by applying Jacobi's form of the least action principle to the vibrationally adiabatic RPH. (c) 2005 American Institute of Physics. [less ▲]

The translational kinetic energy release distribution (KERD) for the halogen loss reaction of the bromobenzene and iodobenzene cations has been reinvestigated on the microsecond time scale. Two necessary ... [more ▼]

The translational kinetic energy release distribution (KERD) for the halogen loss reaction of the bromobenzene and iodobenzene cations has been reinvestigated on the microsecond time scale. Two necessary conditions of validity of the orbiting transition state theory (OTST) for the calculation of kinetic energy release distributions (KERDs) have been formulated. One of them examines the central ion-induced dipole potential approximation. As a second criterion, an adiabatic parameter is derived. The lower the released translational energy and the total angular momentum, the larger the reduced mass, the rotational constant of the molecular fragment, and the polarizability of the released atom, the more valid is the OTST. Only the low-energy dissociation of the iodobenzene ion (E approximately 0.45 eV, where E is the internal energy above the reaction threshold) is found to fulfill the criteria of validity of the OTST. The constraints that act on the dissociation dynamics have been studied by the maximum entropy method. Calculations of entropy deficiencies (which measure the deviation from a microcanonical distribution) show that the pair of fragments does not sample the whole of the phase space that is compatible with the mere specification of the internal energy. The major constraint that results from conservation of angular momentum is related to a reduction of the dimensionality of the dynamics of the translational motion to a two-dimensional space. A second and minor constraint that affects the KERD leads to a suppression of small translational releases, i.e., accounts for threshold behavior. At high internal energies, the effects of curvature of the reaction path and of angular momentum conservation are intricately intermeddled and it is not possible to specify the share of each effect. [less ▲]

The kinetic energy release distributions (KERDs) for the fluorine atom loss from the 1,1-difluoroethene cation have been recorded with two spectrometers in two different energy ranges. A first experiment ... [more ▼]

The kinetic energy release distributions (KERDs) for the fluorine atom loss from the 1,1-difluoroethene cation have been recorded with two spectrometers in two different energy ranges. A first experiment uses dissociative photoionization with the He(I) and Ne(I) resonance lines, providing the ions with a broad internal energy range, up to 7 eV above the dissociation threshold. The second experiment samples the metastable range, and the average ion internal energy is limited to about 0.2 eV above the threshold. In both energy domains, KERDs are found to be bimodal. Each component has been analyzed by the maximum entropy method. The narrow, low kinetic energy components display for both experiments the characteristics of a statistical, simple bond cleavage reaction: constraint equal to the square root of the fragment kinetic energy and ergodicity index higher than 90%. Furthermore, this component is satisfactorily accounted for in the metastable time scale by the orbiting transition state theory. Potential energy surfaces corresponding to the five lowest electronic states of the dissociating 1,1-C2H2F2+ ion have been investigated by ab initio calculations at various levels. The equilibrium geometry of these states, their dissociation energies, and their vibrational wavenumbers have been calculated, and a few conical intersections between these surfaces have been identified. It comes out that the ionic ground state (X) over tilde B-2(1) is adiabatically correlated with the lowest dissociation asymptote. Its potential energy curve increases in a monotonic way along the reaction coordinate, giving rise to the narrow KERD component. Two states embedded in the third photoelectron band ( (B) over tilde (2)A(1), at 15.95 eV and (C) over tilde B-2(2) at 16.17 eV) also correlate with the lowest asymptote at 14.24 eV. We suggest that their repulsive behavior along the reaction coordinate be responsible for the KERD high kinetic energy contribution. [less ▲]

Hydrogen loss from the toluene molecular ion generates benzylium (Bz(+)) and tropylium (Tr+) ions via two competitive and independent pathways. The corresponding kinetic energy release distributions (KERDs) have been determined under various conditions in the metastable time window for toluene and perdeuterated toluene and have been analyzed by the maximum entropy method (MEM). The isomeric fraction Tr+/Bz(+) is found to be equal to 0.9 +/- 0.3, in good agreement with the values obtained using photodissociation and charge exchange experiments. It is, however, in disagreement with the value 5 +/- 2 deduced by Moon, Choe, and Kim (J. Phys. Cheln. A 2000, 104, 458) from KERD measurements. The origin of the discrepancy is suggested to be the inadequacy of the orbiting transition state theory (OTST) for the calculation of KERDs in hydrogen loss reactions. For both channels, more translational energy is released in the reaction coordinate than would be expected on statistical grounds because of the presence of a barrier along the reaction path. For the Bz(+) channel, the barrier entirely results from centrifugal effects. Rotational energy is converted into translation as a result of angular momentum conservation. Deuteration is observed to reduce the importance of the rotational energy flow in the reaction coordinate. The Tr+ channel is characterized by the presence of a reverse activation energy barrier of electronic origin. The energy in excess of the dissociation asymptote can be partitioned into two components: the reverse barrier plus a nonfixed energy contribution. About 40% of the reverse barrier is converted into relative translational motion of the fragments. Here again, a lower fraction of the nonfixed energy flows into translation for the deuterated isotopomer. [less ▲]

in International Journal of Mass Spectrometry (2003), 228(2-3), 389-402

The kinetic energy released to the C4H4+ and HCN fragments produced by the dissociation of the pyridine ion has been determined by a retarding field technique up to an internal energy of 4eV above the ... [more ▼]

The kinetic energy released to the C4H4+ and HCN fragments produced by the dissociation of the pyridine ion has been determined by a retarding field technique up to an internal energy of 4eV above the reaction threshold. This extends our previous study limited to the metastable domain [Int. J. Mass Spectrom. Ion Process. 185/186/187 (1999) 155]. Retarding potential curves resulting from dissociative photoionization using the He(I), Ne(I), and Ar(II) resonance lines have been analyzed by the maximum entropy method. The comparison between the experimentally measured curves and those calculated for the prior (i.e., most statistical) situation reveals the existence of dynamical constraints that prevent phase space from being fully explored. The "ergodicity index" F(E) that measures the efficiency of phase space sampling as a function of the internal energy E of the molecular ion is found to decrease steadily as a function of E and to level off at a value of about 50% when E greater than or equal to 2.5 eV At these high internal energies where phase space exploration no longer decreases, spontaneous intramolecular vibrational energy redistribution (i.e., resulting from the anharmonicity of the molecular vibrations) is thought to contribute to internal energy randomization to a limited extent only. When the lifetime is short, phase space exploration is believed to result instead from the relaxation of the electronic energy via a cascade of non-radiative transitions, which leads to a great diversity of initial conditions, and thus, contributes to statisticity. (C) 2003 Elsevier Science B.V. All rights reserved. [less ▲]

The experimental KER and the statistical distributions are compared by the Maximum Entropy Method. An Ergodicity Index F(E) is defined to measure the phase space sampling efficiency. This is applied to ... [more ▼]

The experimental KER and the statistical distributions are compared by the Maximum Entropy Method. An Ergodicity Index F(E) is defined to measure the phase space sampling efficiency. This is applied to the KERD of C4H4+ cation produced by the C5H5N+ -> HCN+C4H4+ fragmentation path. In this particular case the F(E) is found to decrease steadily with increasing internal energy. [less ▲]

The Orbiting Transition State version of the Phase Space Theory (PST) is used to calculate the KER distributions in the dissociation channel of X (X=I,Cl,Br)-loss from C6H5X+. The results are compared to ... [more ▼]

The Orbiting Transition State version of the Phase Space Theory (PST) is used to calculate the KER distributions in the dissociation channel of X (X=I,Cl,Br)-loss from C6H5X+. The results are compared to the experimental distribution and to that obtained by PST. [less ▲]

We examine the volume of phase space sampled by a nonstationary wave packet when the spectral function consists of a single clump or of a series of them. The relaxation laws are expressed in terms of ... [more ▼]

We examine the volume of phase space sampled by a nonstationary wave packet when the spectral function consists of a single clump or of a series of them. The relaxation laws are expressed in terms of reduced time variables tau, whose definition involves either the average density of states (for a single clump) or appropriately weighted average densities of states (when the spectrum consists of many clumps). Introducing reasonable approximations, very simple generic relaxation laws are derived for the ratio N(tau)/N-infinity which measures the fraction of available phase space that has been sampled by time tau. Under certain assumptions, these laws are found to depend neither on the number nor on the individual features (shapes and widths) of the clumps. However, they strongly depend on the nature (regular or chaotic) of the underlying dynamics. When the dynamics is regular, the relaxation law is expressed in terms of tau(-1), whereas the corresponding equation in the chaotic limit is slightly more complicated and involves terms in tau(-2) and tau(-2) ln tau. Phase space is thus explored according to essentially different relaxation laws in the regular and chaotic limits, the difference being appreciable during the entire relaxation. These laws reflect in the time domain the difference in the distribution of nearest-neighbor level spacings observed in the energy domain (Poisson or Wigner statistics). [less ▲]